# Are Z-shaped cranks a good idea?

I've stumbled across this kickstarter project, which promotes an original shape for cranks:

They claim a wider arc of useful push during rotation. While their main point is rendered moot by clipping systems, I remain unsure about their claim in general.

Can these really have a positive impact on power/torque? Is there any risk due to increased stress on some body parts?

• Any physics student with knowledge of the theory behind τ = r x F can tell you that torque is independent of the shape of the arm used to apply it (only the perpendicular distance to the axis is relevant). Or you can do this thought experiment: This curved bar is rigid. Add another rigid bar between the pedal and the gear axis. Since the construction was rigid and is still rigid, none of the components able to move with respect to each other, this changes nothing. Now remove the curved bar. The construction is still as rigid as before, the dynamics are unchanged. – Joren Oct 9 '12 at 13:48
• It occurs to me that even if their theory were correct, they'd just be stealing from the other side of the arc, and the total would be the same. – Random832 Oct 9 '12 at 17:53
• It definitely allows you to put your toe between the crank and the chain wheel. – wnrph Oct 9 '12 at 18:42
• If I were forced to choose between using these cranks and having "I am gullible" tattooed on my forehead, I'd choose the cranks, although the effect of the two is similar. – Kaz Oct 10 '12 at 4:51
• The people that use these will have something different "tattooed" on their heads as they learn about reduced ground clearance when they crash their bikes by steering the front wheel into the longer crank and when the longer crank touches the ground on cornering or uneven terrain. – bmike Oct 10 '12 at 18:18

If the aluminum is sufficiently stiff it makes zero difference -- the crank could be any shape (a disk, an S shape, etc), but the relationship between the two contact points would still remain the same, and that's all that counts.

The only effect the crank could have is adding a bit of spring to the crank, which might be good or bad for effective cranking. But aluminum makes lousy springs, and if it flexes much it will soon fatigue and fail.

The risk to your body parts is getting cut by sharp edges when the crank fails.

• This is my thought too. If the crank is stiff, the shape of the crank doesn't matter. Look at the video at 0:52, where it compares the two cranks in the same picture with the green overlay. Look at the Z-torque top angle and think about which direction the force would have to be to move that crank. With the position of foot on the top of the arc, pushing down on the pedal would turn the cranks backwards, in order to move them forwards, you would have to move your foot horizontal to the ground. Also if you want to convince me, show me the data from the university study. – Kibbee Oct 9 '12 at 12:59
• I wonder if it'd be possible to make something similar out of spring steel, to actually take advantage of the spring effect? Also, my pants already get caught on my straight cranks. These cranks look terrifying. – naught101 Oct 10 '12 at 6:24
• I'm sure people have tried spring steel in the past -- the "modern" bike has been around for well over 100 years and just about everything's been tried. What may not have been well tried is a slightly springy crank arm, vs one with a lot of spring. But with any such design you have trouble with the arm twisting and cocking the angle of the pedal. Also, it's very hard to effectively test such devices, due to the placebo effect. – Daniel R Hicks Oct 10 '12 at 11:31
• Also, springs are never 100% efficient, so you'd get a spongy crank and a (probably small) power loss. – freiheit Oct 10 '12 at 20:32
• Add the extra weight for all the excess aluminum and you are losing any advantage they are trying to sell you! – BillyNair Oct 11 '12 at 20:26

The comments on the Kickstarter project have a few good explanations of both why the design is effectively identical to a straight crank, and why the plan to make carbon-fiber versions is dangerous.

Now leverage: if you tried to push down on the pedal (as shown in the video) when it was exactly top dead center and stopped, it doesn't matter if it is a normal crank or the Z-Torque, it will not want to move. They are two rigidly attached points in space, so it doesn't matter WHAT you use to connect them, 'physics' just treats them as though connected by a straight bar.

Simple proof: If you move the Z-torque back just 2 degrees before top dead center and apply a force (you could try with a weight rather than a foot to make it scientifically valid), you will see that it doesn't move FORWARD as would happen if your crank worked as you argue (advancing the leverage because of the bend), but still BACKWARDS the exact same as a normal crank.

It looks different but it works THE SAME.

..and why it is dangerous:

2) You absolutely cannot take a design that is optimized for machining "mold them out of carbon fiber". Woven composite strength is highly anisotropic. If anything, your design shown in your picture is weaker, not stronger, than the machined part, if molded out of carbon fiber (and by that I assume you mean, "molded out of cast polymer with a carbon fiber veneer on the front surface).

A true carbon fiber crank would have the fiber direction laid out (often by hand) in such a way that the fiber direction (or grain direction) aligns with the force exerted on the piece. So all that ladder structure that you've molded into the part,would actually make it a LOT weaker. It would also have machined metal components laid into the part and bonded to the composites for a metal-on-metal mating surface. See http://www.zipp.com/support/identify/carbon_cranks.php for an example of the construction technique - note the use of an aluminum spider that the actual crank is bonded to.

[...]

5) Finally, and the most worrying point: You are dealing with an important piece of a bike's drive train. The failure mode on this is likely going to be the a cyclist cranking away and your crank giving way and breaking off. This is the makings of a serious, and possibly life altering accident.

Non-destructive testing and examination of composite materials is no joke. I can assure you that the folks from Shimano and RaceFace has years of experience building, validating and testing composite structures that they built. The failure modes of composite materials is also very different than traditional metal - there is very little to none inelastic deformation.

The mold and setup you show is good for producing cosmetic composite components (like my buddy's "Carbon fiber" gas and brake pedal). A mission critical drive train piece, not so much.

The complete comment is worth reading.

• What's interesting is that the person who posted this, "Terence Tam" is also on the list of backers. – Kibbee Oct 9 '12 at 15:14
• @Kibbee: you can't post unless you back. He likely backed a small amount to be able to warn others, which is rather altruistic of him. – Roy Tinker Oct 9 '12 at 16:32
• @RoyTinker I've never used Kickstarter before, but that's quite a big problem. Only people who (financially) support a product are allowed to comment about it? I guess you don't want a ton of youtube quality comments flooding every kickstarter project, but there needs to some method for people to discuss the viability of a project before they put their money on the line. – Kibbee Oct 9 '12 at 17:05
• @Kibbee: Most projects allow 1\$ as a minimum pledge and you won't actually have to pay it unless the project gets 100% funding so it probably isn't that big of a problem (although I do agree that there should be some way of discussing the viability without having to put any money in). – Leo Oct 9 '12 at 18:18

This is just a rehashing of a very old and horrible idea. See PMP Cranks et al.

RE: PMP cranks

A moment's thought shows a straight crank and an L crank always have the same relation between pedals, chain, and bottom bracket. Thus, there is no advantage to L cranks. And an L crank always has more material than a straight crank, so is always at a disadvantage for weight, strength, stiffness, and/or cost.

The P.M.P. cranks have a spider bolted to the right crank, with the square taper formed from both pieces. The square taper is loaded heavily, and making it in pieces, especially with a few light bolts to hold them together, is likely to increase loads greatly and thus lead to premature failures. So it may be unwise to ride these, even for art or humor value.

RE: Z Torque cranks

The Z Torque crank manages to take a bad idea and make it worse: the crank spider is not simply bolted to the right arm. Instead, it is about 1/3 of the square taper, while the arm is the other 2/3. This puts a joint in the middle of a highly-stressed joint — so highly stressed that hardened steel spindles sometimes break here.

Z-Torque also has much less ground clearance than a straight crank, much less even than a P.M.P. crank.

And then there is this from their own video:

Participants achieved similar maximal oxygen consumption, peak power outputs and gross efficiencies with the Z-Torque and normal crank configurations (Table 1). In addition, ratings of perceived exertion (RPE) at 150 and 200 W, heart rate (HR) at peak power output, 150, and 200 W, and cadence at 150 and 200 W were not significantly different. However, participants perceived their effort to be significantly lower at peak power output with the Z-Torque crank.

Even their own study and material showed no significant difference between the Z crank and a normal crank. The "perceived" notion is flawed because it is not a blind/double blind test.

• If you read through the link I provided, you will also find an additional link to information on Z torque cranks themselves. Outside of all the other physics data provided in other posts in this question, the issue of ground clearance is huge. There is far less ground clearance on these cranks making pedal (or an unheard of arm) strike a real and distinct possibility for even the slightest of turns. – Tha Riddla Oct 9 '12 at 14:27
• Another article on the history (content has overlap with your link): road.cc/content/feature/… – armb Mar 15 '18 at 14:30

Unfortunately this doesn't help. The example pictures demonstrate misunderstanding elementary classical mechanics and more specifically, statics. Moment, a.k.a. torque, is defined as

``````M = F * d
``````

where

``````F = the force applied
d = the perpendicular distance from the axis to the line of action of the force.
``````

The shape of the crank has not effect on either. `F` is the force coming from the leg/foot, and `d` is defined solely by the distance between pedal and hub, multiplied by sine of the angle between `F` and the vector defined by the pedal and the hub.

In the second example picture,

the pushing hand is misleadingly positioned forward so that `d` is increased, and that will increase moment. However, the pedal is straight above the hub, so pushing downward still creates a zero moment.

If the normal crank is `A`, do you think adding arms `B` and `C` and would make a difference (except adding mass)? Remove `A`, and you have a "Z-shaped" system.

• Yours is my favorite response. I remember this rigid-body torque question from Statics in college. The prof came up with a dozen different complicated designs for the same idea... "the sum of the forces equals zero". It doesn't matter what the shape of the arm is. (Except, of course, the weight of the new shape will cause some negligible torque in this position, but that will get zeroed out by a different position in the cycle.) Good explanation! – Brian Genisio Oct 10 '12 at 19:22

It just adds extra weight and probably is less reliable due to increased flexing. The "lever arm" for mechanical advantage is the same as it would be for an arm that went straight to the pedal. This is like those adverts for "male enhancement".

This design adds nothing new, many cranks similar to this have been developed during the 100+ years of cycle design and all have failed to achieve the supposed power advantage and become mainstream.

Buy this if you like the look and feel of flex at the pedal spindle buy it.

No.

• You have less room for the front wheel to turn when the longest part of the crank is horizontal to the ground.

• You have less ground clearance when the longest part of the crank is closest to the ground.

• Flex always loses power, and even if these were perfectly stiff, there is no mechanical advantage since force is not applied on the end of the Z but instead in the same place as a traditional crank.

These cranks are however perfect for cranks (eccentric people) or scrapers that want some bling and don't care about safety or efficiency.